End-stage renal disease (ESRD) and other forms of organ failure have become a major public health concern in the United States due to their mortality, morbidity and associated health care costs. Due to increased incidence, the demand for donor organs has eclipsed the supply and the appropriate allocation of the scarce supply of donor organs is a hotly contended issue. This project addresses several fundamental questions on organ failure which cannot be addressed using existing failure time methods. In Aim 1, we propose survival analysis methods for estimating the transplant survival benefit (i.e., contrast between wait-list and post-transplant mortality) when such benefit interacts with another time-dependent covariate. The methods view the data structure from a novel perspective and the resulting parameter estimates have a much improved interpretation relative to the existing models. In Aim 2, we develop random effects additive rates models for recurrent event data. For a multi-center study, the proposed methods permit the statistical inference to apply to the population of centers from which those in the study were selected. The model parameters have a much improved interpretation relative to existing multiplicative rates models. Weighted regression models for are developed in Aim 3. The proposed models can be applied to unrepresentative samples and, unlike existing weighted Cox models, will be valid when the sample inclusion probabilities are not known and must be estimated from the data. Methods for center-specific outcomes are proposed in Aim 4. We develop and evaluate methods to compare center-specific (i) mortality and (ii) transplant benefit. The mortality methods propose novel and easily interpretable summary statistics to describe and test the center effects. The methods for transplant benefit are valid in the presence of interactions between transplant and other covariates.